A disc of mass 4 kg and radius 6 m is free to rotate in a horizontal plane about a vertical fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small

Question

A disc of mass 4 kg and radius 6 m is free to rotate in a horizontal plane about a vertical fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass 2 kg each are placed in it on either side of the centre of the disc as shown in figure. The disc is given initial angular velocity $ω_{0} = 12$ rad/s and released. Find the angular speed of disc (in rad/s) when the balls reach the ends of the disc.

TestHub · Accepted Answer

No external torque, so angular momentum is conserved 2 M R 2 ​ ω 0 ​ = [ 2 M R 2 ​ + 2 m R 2 ] ω f ​ M = 4 kg, m = 2 kg 72 × 12 = ( 72 + 144 ) ω f ​ ω f ​ = 4 rad/s Answer: 4

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